Is an iphone unlocked if there's no service?

I got a iphone from someone, which was originally sprint and it had sprint displayed on the top left corner. Then I restored it and know the sprint displayed on top is gone. What does this mean, is it unlocked?

Means it has a bad esn and is useless as a phone

It's prob been barred which means its useless

In most cases your iPhone can only be unlocked by the network provider itself, if certain requirements are met (ie.using it for international travelling). Verizon sells their iPhone 5s unlocked but that's a rare decision across providers. That said, it's highly unlikely that your iPhone is unlocked purely by restoring it.

Also, Sprint works with a CDMA network, so if you are still in the United States, you can only use their phones on Verizon or Sprint, but not any other providers.

Did a quick digup - Sprint definitely does not unlock iPhones for domestic use. See attached source links.

Nope, it means the phone is not picking up any signal now and the seller might've deactivated the phone. You can try to get the phone activated on Sprint if you're on Sprint. If you want to use the phone on other carrier, get the phone flashed or unlocked if it's iPhone 4S or 5. You can mail this person (arghyle@rocketmail.com) who can help you with the flashing or unlocking whichever you'll require.